Homeostasis in networks with multiple inputs

Homeostasis, also known as adaptation, refers to the ability of a system to counteract persistent external disturbances and tightly control the output of a key observable. Existing studies on homeostasis in network dynamics have mainly focused on 'perfect adaptation' in deterministic single-input single-output networks where the disturbances are scalar and affect the network dynamics via a pre-specified input node. In this paper we provide a full classification of all possible network topologies capable of generating infinitesimal homeostasis in arbitrarily large and complex multiple inputs networks. Working in the framework of 'infinitesimal homeostasis' allows us to make no assumption about how the components are interconnected and the functional form of the associated differential equations, apart from being compatible with the network architecture. Remarkably, we show that there are just three distinct 'mechanisms' that generate infinitesimal homeostasis. Each of these three mechanisms generates a rich class of well-defined network topologies-called homeostasis subnetworks. More importantly, we show that these classes of homeostasis subnetworks provides a topological basis for the classification of 'homeostasis types': the full set of all possible multiple inputs networks can be uniquely decomposed into these special homeostasis subnetworks. We illustrate our results with some simple abstract examples and a biologically realistic model for the co-regulation of calcium ( Ca ) and phosphate ( PO 4 ) in the rat. Furthermore, we identify a new phenomenon that occurs in the multiple input setting, that we call homeostasis mode interaction, in analogy with the well-known characteristic of multiparameter bifurcation theory.

Modeling the Progression of Cardiac Catecholamine Deficiency in Lewy Body Diseases

Background Lewy body diseases (LBDs) feature deficiency of the sympathetic neurotransmitter norepinephrine in the left ventricular myocardium and sympathetic intra-neuronal deposition of the protein alpha-synuclein (αS). LBDs therefore are autonomic synucleinopathies. Computational modeling has revealed multiple functional abnormalities in residual myocardial sympathetic noradrenergic nerves in LBDs, including decreased norepinephrine synthesis, vesicular storage, and recycling. We report an extended model that enables predictions about the progression of LBDs and effects of genetic predispositions and treatments on that progression. Methods and Results The model combines cardiac sympathetic activation with autotoxicity mediated by the dopamine metabolite 3,4-dihydroxyphenylacetaldehyde. We tested the model by its ability to predict longitudinal empirical data based on cardiac sympathetic neuroimaging, effects of genetic variations related to particular intra-neuronal reactions, treatment by monoamine oxidase inhibition to decrease 3,4-dihydroxyphenylacetaldehyde production, and post-mortem myocardial tissue contents of catecholamines and αS. The new model generated a triphasic decline in myocardial norepinephrine content. This pattern was confirmed by empirical data from serial cardiac 18F-dopamine positron emission tomographic scanning in patients with LBDs. The model also correctly predicted empirical data about effects of genetic variants and monoamine oxidase inhibition and about myocardial levels of catecholamines and αS. Conclusions The present computational model predicts a triphasic decline in myocardial norepinephrine content as LBDs progress. According to the model, disease-modifying interventions begun at the transition from the first to the second phase delay the onset of symptomatic disease. Computational modeling coupled with biomarkers of preclinical autonomic synucleinopathy may enable early detection and more effective treatment of LBDs.

A homeostasis criterion for limit cycle systems based on infinitesimal shape response curves

Homeostasis occurs in a control system when a quantity remains approximately constant as a parameter, representing an external perturbation, varies over some range. Golubitsky and Stewart (J Math Biol 74(1-2):387-407, 2017) developed a notion of infinitesimal homeostasis for equilibrium systems using singularity theory. Rhythmic physiological systems (breathing, locomotion, feeding) maintain homeostasis through control of large-amplitude limit cycles rather than equilibrium points. Here we take an initial step to study (infinitesimal) homeostasis for limit-cycle systems in terms of the average of a quantity taken around the limit cycle. We apply the "infinitesimal shape response curve" (iSRC) introduced by Wang et al. (SIAM J Appl Dyn Syst 82(7):1-43, 2021) to study infinitesimal homeostasis for limit-cycle systems in terms of the mean value of a quantity of interest, averaged around the limit cycle. Using the iSRC, which captures the linearized shape displacement of an oscillator upon a static perturbation, we provide a formula for the derivative of the averaged quantity with respect to the control parameter. Our expression allows one to identify homeostasis points for limit cycle systems in the averaging sense. We demonstrate in the Hodgkin-Huxley model and in a metabolic regulatory network model that the iSRC-based method provides an accurate representation of the sensitivity of averaged quantities.

Homeostatic model of human thermoregulation with bi-stability

All homoiothermic organisms are capable of maintaining a stable body temperature using various negative feedback mechanisms. However, current models cannot satisfactorily describe the thermal adaptation of homoiothermic living systems in a physiologically meaningful way. Previously, we introduced stress entropic load, a novel variable designed to quantify adaptation costs, i.e. the stress of the organism, using a thermodynamic approach. In this study, we use stress entropic load as a starting point for the construction of a novel dynamical model of human thermoregulation. This model exhibits bi-stable mechanisms, a physiologically plausible features which has thus far not been demonstrated using a mathematical model. This finding allows us to predict critical points at which a living system, in this case a human body, may proceed towards two stabilities, only one of which is compatible with being alive. In the future, this may allow us to quantify not only the direction but rather the extent of therapeutic intervention in critical care patients.

Homeostasis, singularities, and networks

Homeostasis occurs in a biological or chemical system when some output variable remains approximately constant as an input parameter [Formula: see text] varies over some interval. We discuss two main aspects of homeostasis, both related to the effect of coordinate changes on the input-output map. The first is a reformulation of homeostasis in the context of singularity theory, achieved by replacing 'approximately constant over an interval' by 'zero derivative of the output with respect to the input at a point'. Unfolding theory then classifies all small perturbations of the input-output function. In particular, the 'chair' singularity, which is especially important in applications, is discussed in detail. Its normal form and universal unfolding [Formula: see text] is derived and the region of approximate homeostasis is deduced. The results are motivated by data on thermoregulation in two species of opossum and the spiny rat. We give a formula for finding chair points in mathematical models by implicit differentiation and apply it to a model of lateral inhibition. The second asks when homeostasis is invariant under appropriate coordinate changes. This is false in general, but for network dynamics there is a natural class of coordinate changes: those that preserve the network structure. We characterize those nodes of a given network for which homeostasis is invariant under such changes. This characterization is determined combinatorially by the network topology.

Escape from homeostasis

Many physiological systems, from gene networks to biochemistry to whole organism physiology, exhibit homeostatic mechanisms that keep certain variables within a fairly narrow range. Because homeostatic mechanisms buffer traits against environmental and genetic variation they allow the accumulation of cryptic genetic variation. Homeostatic mechanisms are never perfect and can be destabilized by mutations in genes that alter the kinetics of the underlying mechanism. We use mathematical models to study five diverse mechanisms of homeostasis: thermoregulation; maintenance of homocysteine concentration; neural control by a feed forward circuit; the myogenic response in the kidney; and regulation of extracellular dopamine levels in the brain. In all these cases there are homeostatic regions where the trait is relatively insensitive to genetic or environmental variation, flanked by regions where it is sensitive. Moreover, mutations or environmental changes can place an individual closer to the edge of the homeostatic region, thus predisposing that individual to deleterious effects caused by additional mutations or environmental changes. Mutations and environmental variables can also reduce the size of the homeostatic region, thus releasing potentially deleterious cryptic genetic variation. These considerations of mutations, environment, homeostasis, and escape from homeostasis help to explain why the etiology of so many diseases is complex.

Activity pattern of the neotropical marsupial Didelphis aurita in south-eastern Brazilian Atlantic Forest

Nocturnal activity is generally presumed, but rarely evaluated in studies of tropical small mammals. When evaluated, activity is frequently presented as a fixed pattern, but actually it is the influence of biotic and abiotic factors on individuals. We investigated effects of age, sex, minimum temperature, reproductive and climatic seasons on activity of Didelphis aurita (Didelphimorphia, Didelphidae) in an Atlantic Forest area in south-eastern Brazil from June 2009 to December 2010. We captured 37 individuals, 51 times (28 females and 23 males). Activity of D. aurita was mostly nocturnal, but some individuals were active during the day (12%, N = 6). Nocturnal activity was bimodal, more prevalent in adults than juveniles, and different from most neotropical marsupials. Contrary to expectations, individuals of D. aurita were more active at colder temperatures, which indicates that low temperatures do not limit foraging behaviour.